We instead turn to iterative search methods to try to achieve the best possible solution, using HOEVD as an initialization.
For Tucker decomposition, Newton [1]}, [2]}, quasi-Newton [3]} and trust-region [4]} methods have been considered. These second-order optimization approaches rely on sophisticated updates on manifolds, based on Riemannian gradient and Hessian computations. Higher-order orthogonal iterations (HOOI) [5]}, Jacobi rotations [6]}, [7]} and the power method [8]} have been proposed for symmetric tensors.
Among these, the power method does not always converge, as shown in numerical examples of [8]}.
Regalia briefly mentions a shifted variant of the power method in [8]}, which is akin to a gradient descent method, although strong convergence analysis is omitted in the work.
